An efficient parallel algorithm for Caputo fractional reaction-diffusion equation with implicit finite-difference method is proposed in this paper. The parallel algorithm consists of a parallel solver for linear tridiagonal equations and parallel vector arithmetic operations. For the parallel solver, in order to solve the linear tridiagonal equations efficiently, a new tridiagonal reduced system is developed with an elimination method. The experimental results show that the parallel algorithm is in good agreement with the analytic solution. The parallel implementation with 16 parallel processes on two eight-core Intel Xeon E5-2670 CPUs is 14.55 times faster than the serial one on single Xeon E5-2670 core.

In this paper, we develop a novel structured mesh generation method, MeshNet. The core of the proposed method is the introduction of deep neural networks to learn high-quality meshing rules and generate desired meshes. To accomplish this, MeshNet employs a well-designed physics-informed neural network to approximate the potential transformation (mapping) between computational and physical domains. The training process is governed by differential equations, boundary conditions, and a priori data derived from coarse mesh generation, which has been disregarded in previous studies. The automatic subdivision of a given domain into quadrilateral elements is achieved through efficient feed-forward neural prediction. A series of experiments are conducted to investigate the robustness of the proposed method. The results across different cases demonstrate that MeshNet is fast and robust. It outperforms state-of-the-art neural network-based generators and produces meshes of comparable or higher quality compared to expensive traditional meshing methods. Furthermore, the proposed method enables fast varisized mesh generation without re-training. The simplicity and computational efficiency of MeshNet make it a novel meshing tool in the discretization part of simulation software.

The sigmoid activation function is popular in neural networks, but its complexity limits the hardware implementation and speed. In this paper, we use curvature values to divide the sigmoid function into different segments and employ the least squares method to solve the expressions of the piecewise linear fitting function in each segment. We then adopt an optimization method with maximum absolute errors and average absolute errors to select an appropriate function expression with a specified number of segments. Finally, we implement the sigmoid function on the field-programmable gate array (FPGA) development platform and apply parallel operations of arithmetic (multiplying and adding) and range selection at the same time. The FPGA implementation results show that the clock frequency of our design is up to 208.3 MHz, while the end-to-end latency is just 9.6 ns. Our piecewise linear fitting method based on curvature analysis (PWLC) achieves recognition accuracy on the MNIST dataset of 97.51% with a deep neural network (DNN) and 98.65% with a convolutional neural network (CNN). Experimental results demonstrate that our FPGA design of sigmoid function can obtain the lowest latency, reduce absolute errors, and achieve high recognition accuracies, while the hardware cost is acceptable in practical applications.

With growing scale of the data volume and neural network size, we have come into the era of distributed deep learning. High-performance training and inference on distributed computing systems has been attracting increasing research attention in both academia and industry. Meanwhile, diversity of existing machine learning frameworks (e.g. TensorFlow, Pytorch and MXNet) and the explosion of deep learning hardwares (e.g. CPUs, GPUs, FPGAs and ASICs) bring more challenges for users to leverage new deep learning technologies and accelerating capability of hardware devices. We firstly search around the state-of-the-art work in the area which open our mind to take a vision upon the future deep learning framework. Then, we propose HPDL, a general framework for high-performance distributed deep learning which is compatible with existing frameworks and adaptive to various hardware architectures. At last, we discuss and foresee the key technologies fulfilling high-performance and large-scale deep learning, including optimization algorithm, hybrid communication mechanism, model parallelization, resource scheduling and single-node execution optimization.